Structural and dynamical properties of inclusion complexes compounds and the solvents from ¯rst-principles investigations Von der FakultÄat furÄ Naturwissenschaften der UniversitÄat Duisburg-Essen (Standort Duisburg) zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften (Dr. rer.nat.) genehmigte Dissertation von Waheed Adeniyi Adeagbo aus Ibadan, Oyo State, Nigeria Referent: Prof. Dr. P. Entel Korreferent: PD. Dr. A. BaumgÄartner Tag der mundlicÄ hen Prufung:Ä 20 April 2004 3 Abstract In this work, a series of ab-initio calculations based on density functional theory is presen- ted. We investigated the properties of water and the inclusion complexes of cyclodextrins with various guest compounds such as phenol, aspirin, pinacyanol chloride dye and bi- naphtyl molecules in the environment of water as solvent. Our investigation of water includes the cluster units of water, the bulk properties of the li- quid water and the crystalline ice structure. Some equilibrium structures of water clusters were prepared and their binding energies were calculated with the self-consistency den- sity functional tight binding (SCC-DFTB) method. The global minimum water clusters of TIP4P classical modelled potential were also calculated using the DFTB method and Vienna Ab-initio Simulation Package (VASP). All results show a non-linear behaviour of the binding energy per water molecule against water cluster size with some anomalies found for the lower clusters between 4 and 8 molecules. We also calculated the melting temperatures of these water clusters having solid-like behaviour by heating. Though, the melting region of the heated structures is not well de¯ned as a result of the pronoun- ced uctuations of the bonding network of the system giving rise to uctuations in the observed properties, but nevertheless the range where the breakdown occurs was de¯- ned as the melting temperature of the clusters. The bulk properties of the liquid, such as radial distribution functions, calculated with the VASP method show good agreement with neutron di®raction scattering data with respect to positions and height of the peaks. The DFTB method gives good positions of the peaks but with too broad peaks due the approximations on which the method relies, which makes it less accurate. Due to the com- plexity of the hydrogen bonding network, it is di±cult to obtain the real ice structure by mere cooling liquid water under normal condition without imposing external constraints such as extreme external pressure or electric ¯eld. A special rule of proton ordering was followed in order to prepare the real ice structure for our calculations. We succeeded in preparing a hexagonal tetrahedrally coordinated type of ice. The statical properties of this ice were calculated as well as the phonon spectra. The results were compared with neutron di®raction data and other available ab-initio calculations. The molecular dynamics simulations of inclusion complexes of ¯-cyclodextrin with each of these guest molecules, phenol and aspirin show the encapsulation which are in good agreement with dichroism measurements. The inclusion complex of a dimer calculation of pinacyanol dye with some droplet of water inside -cyclodextrin shows structural pro- perties which can be ascribed to the experimental observation of UV/CD spectra of the chromophores, in which there is a split of the excited states of the monomer units. The calculations on chiral molecules of binaphtyl-¯-cyclodextrin complex shows a longitudinal axis as preferred axis of entry of the binaphtyl during the inclusion process rather than an axial propagation in agreement with circular dichroism measurements. The investigated chiral separation ability of ¯-cyclodextrin on the enantiomeric pair of this compound R and S, which di®er in symmetry only by reection, shows that the S-enantiomer has lower energy than the R-enantiomer as revealed by our ab-initio calculations. 4 5 Contents Abstract 4 Contents 5 List of Figures 8 List of Tables 12 1 Introduction 13 1.1 Biological and organic molecules . 13 1.2 Computer simulations . 16 1.3 Objective of this work . 18 2 The density functional theory formalism 21 2.1 Introduction and importance . 21 2.1.1 General foundation . 21 2.1.2 Born-Oppenheimer approximation . 22 2.2 Representation of electronic structure and various approximations . 24 2.2.1 The Hohenberg-Kohn theorem . 25 2.2.2 The basic Kohn-Sham equations . 28 2.3 Approximation for the exchange-correlation energy . 32 2.3.1 Local density approximation . 33 2.3.2 Generalized gradient approximation . 34 2.4 Basis set expansions and pseudopotentials . 35 2.4.1 Plane-wave basis set . 35 2.4.2 The pseudopotential approximation . 37 2.4.3 Norm-conserving pseudopotentials . 39 2.4.4 Non-local and Kleinman-Bylander pseudopotentials . 40 2.4.5 Boundary conditions within the plane-wave description . 43 2.4.6 Slater-type and Gaussian atomic-like orbitals . 44 2.4.7 Self-consistency condition . 45 3 Tight-binding methods 47 3.1 Derivation of the tight-binding model . 47 3.1.1 The Slater-Koster scheme . 49 3.2 The density-functional basis of the tight-binding method (DFTB) . 51 3.2.1 Zeroth-order non-self-consistent charge approach, standard DFTB 53 3.2.2 Second-order self consistent charge extension, SCC-DFTB . 55 6 Contents 4 Molecular dynamics simulation 59 4.1 Minimization . 59 4.2 Conjugate gradient algorithm . 60 4.3 Molecular dynamics algorithm . 61 4.4 How the temperature is calculated . 65 4.5 How the temperature is controlled . 67 4.5.1 Direct velocity scaling . 68 4.5.2 Berendsen's method of temperature-bath coupling . 68 4.5.3 Nos¶e dynamics . 68 4.6 Measured observables from ab-initio molecular dynamics . 69 4.6.1 Static properties . 70 4.6.2 Dynamical properties . 72 4.6.3 Geometrical properties . 73 5 Water clusters and their transition temperatures 75 5.1 Water clusters . 75 5.1.1 Investigation of the water dimer, (H2O)n, n = 2 . 76 5.1.2 Binding energy of water clusters for n > 2 . 77 5.1.3 Melting temperature of water clusters . 78 6 Liquid water and other hydrogen bonding solvents 99 6.1 Some general features of water . 99 6.2 Calculated electronic density of liquid water . 100 6.3 Molecular dynamics study of liquid water . 100 6.3.1 Properties of liquid water at various temperatures . 102 6.3.2 Spectral analysis of liquid water . 109 6.4 Molecular dynamics study of crystalline ice structure . 109 6.5 Lattice dynamical properties of ice . 116 6.5.1 Phonon calculation of ice . 116 6.5.2 Phonons and related properties of the crystal ice . 120 6.5.3 How to calculate LO/TO splitting . 123 6.5.4 Vibrational density of state . 124 6.5.5 The boson peak in ice . 128 6.6 Methanol structural properties . 130 7 A ¯rst-principles study of inclusion complexes of cyclodextrins 133 7.1 Introduction to cyclodextrins . 133 7.2 Some useful applications of cyclodextrins . 136 7.3 Inclusion complexes of cyclodextrins . 136 7.3.1 Inclusion complex with phenol . 137 7.3.2 Inclusion complex with aspirin . 138 7.3.3 Inclusion complex with organic dyes . 141 7.3.4 Inclusion complex with binaphthyl compound . 146 Contents 7 7.3.5 Chiral discrimination of binaphthyl by ¯-cyclodextrin . 155 Summary 161 A Appendix 165 A.1 Theory of lattice dynamics and phonon calculation . 165 A.2 The many phases of ice . 169 A.2.1 Ice Ih . 169 A.2.2 Ice Ic . 171 A.2.3 Amorphous ice . 172 A.2.4 Higher phases of ice . 172 A.3 Thermal properties of ice . 175 References 178 Acknowledgements 195 Curriculum Vitae 197 List of publications 199 8 List of Figures 1.1 Ice structure . 15 1.2 The ¯rst three family members of cyclodextrins . 16 2.1 Full all-electronic wavefunction and electronic potential . 38 3.1 Hopping integrals between two carbon atoms . 50 3.2 Hopping integrals between s and p . 51 4.1 Steepest-descent and conjugate-gradient method . 61 4.2 Flow chart describing the molecular dynamics algorithm. 63 4.3 Representation of two energy minima separated by a barrier in simulated annealing. 65 4.4 Removal of excess heat by simulated annealing method on 32 molecules of water. 66 4.5 Geometrical de¯nition of (a) bond length, (b) angle and (c) dihedral angle. 74 5.1 Stable water dimer geometries for DFTB and VASP studies. 76 5.2 Variation of binding energy of dimer cluster of water with O-O distance. 77 5.3 Initial con¯gurations for some selected water clusters prepared with DFTB . 79 5.4 Initial global minimum con¯gurations for some water clusters . 80 5.5 Variation of binding energy per water molecule as a function of cluster size. 83 5.6 Supercell and binding energy of water pentamer . 84 5.7 Van der Waals like loop de¯ning a ¯rst-order-like transition. 85 5.8 Dihedral angles used in de¯ning ring puckering in water clusters. 86 5.9 Plots of the E against T together with ±OO for water cluster with n = 3, 4, 5 and 6. 87 5.10 Plots of the radial distribution function near melting for water cluster with n = 5, 12, 20 and 36. 89 5.11 Plots of the E against T together with ±OO for water cluster with n = 18, 20, 30 and 36. 90 5.12 Plot of the radial distribution functions near melting for water cluster with n = 5, 12, 20 and 36. 91 5.13 Compared melting temperatures for di®erent methods of calculation . 93 5.14 Energy and ±OO(T ) versus temperature, T(K), for global minimum geometry of TIP4P for n = 3, 4 and 5.